Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -18}$ ${-3x-2y = -16}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-3x-3y = -18}$ $3x+2y = 16$ Add the top and bottom equations together. $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-3x-3y = -18}\thinspace$ to find $x$ ${-3x - 3}{(2)}{= -18}$ $-3x-6 = -18$ $-3x-6{+6} = -18{+6}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 2}$ into $\thinspace {-3x-2y = -16}\thinspace$ and get the same answer for $x$ : ${-3x - 2}{(2)}{= -16}$ ${x = 4}$